Solve a=2b(c-d)

$$a = 2 b ( c - d )$$

Solve for b

$$\left\{\begin{matrix}b=\frac{a}{2\left(c-d\right)}\text{, }&c\neq d\\b\in \mathrm{R}\text{, }&a=0\text{ and }c=d\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2b by c-d.

$$a=2bc-2db$$

Swap sides so that all variable terms are on the left hand side.

$$2bc-2db=a$$

Combine all terms containing b.

$$\left(2c-2d\right)b=a$$

Divide both sides by 2c-2d.

$$\frac{\left(2c-2d\right)b}{2c-2d}=\frac{a}{2c-2d}$$

Dividing by 2c-2d undoes the multiplication by 2c-2d.

$$b=\frac{a}{2c-2d}$$

Divide a by 2c-2d.

$$b=\frac{a}{2\left(c-d\right)}$$

Solve for a

$$a=2b\left(c-d\right)$$